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arXiv · 2105.13526

The Borel Cohomology of Free Iterated Loop Spaces

Ishan Levy·Justin Wu
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Abstract

We compute the $\rm{SO}(n+1)$-equivariant mod $2$ Borel cohomology of the free iterated loop space $Z^{S^n}$ when $Z$ is a mod $2$ generalized Eilenberg Mac Lane space. When $n=1$, this recovers B\"okstedt and Ottosen's computation for the free loop space. The highlight of our computation is a construction of cohomology classes using an $\mathrm{O}(n)$-equivariant evaluation map and a pushforward map.

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Ishan Levy, Justin Wu. 2021-05-28. The Borel Cohomology of Free Iterated Loop Spaces. https://doi.org/10.2140/agt.2026.26.1

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